In table REF  one can see that the ADM mass is highest at \(\xi =-0.12\)  and decreases afterwards as \(\xi \)  increases towards \(\xi =0.095\) . There is one case that does not follow this trend in masses. The ADM mass at \(\xi =-0.14\)  is actually lower than the mass at \(\xi =-0.12\)  (the data points of mass vs. \(\xi \)  is plotted in fig. MPlot and the curve illustrates nicely the trend in masses). The case \(\xi =-0.14\)  has the highest VEV which would seem to imply that it should have the highest mass (vortices with higher VEV will usually have more mass in fixed Minkowski spacetime [1]}). Why then is the mass lower for \(\xi =-0.14\)  than for \(\xi =-0.12\) ? This is due to the fact that the ADM mass receives contributions not only from matter but also from the negative binding energy of the gravitational field (see section 3.9 on “Thin-shell collapse" in [2]} for a clear illustration of this). The metric field \(A(r)\)  near the origin for \(\xi =-0.14\)  (fig. REF ) has a more pronounced dip than for \(\xi =-0.12\)  (fig. REF ). So the negative gravitational binding energy is significant enough in \(\xi =-0.14\)  to yield a lower ADM mass than in \(\xi =-0.12\) .
